How do new springs behave if the opposite axle has older springs? I thought that it would be a taboo swap and that new components are preferred.

No it is not taboo to switch the rear springs as long as nothing is wrong with the front. While the two are related since they are on the same car, the suspension set ups front and rear on the 1 series (as with many other cars) are different. The front has struts (shocks and springs together) while the rear has separate shocks and springs.

Apparently BMW figured out beginning in the 2011 model year that linear springs worked better on the rear of the car than the progressive springs it had been using. I personally agree with the change since I found the progressive rear springs on my 2009 M Sport 135i too soft, especially with the stock rear shocks. When I switched to 2011 M Sport springs in the rear of the car and Koni Sport adjustable dampers all around the car became much more composed and the extreme up and down movement in the rear suspension for the most part went away.

The real key is how the front struts and the rear springs/shocks match up with each other in terms of overall damping. The front of the 1 series typically has softer springs because they are part of the struts. The rear has firmer springs since they are separate from the shocks. While the newer linear (and I believe firmer) rear springs are better than the prior progressive springs, a good set of aftermarket dampers (shocks and struts) will make the car handle even better.